Logarithms
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Logarithms
This is just another word for index or power. So 3^{2} = 9 means the logarithm is 2, with base 3 gives 9.
This can also be written as 2 = log_{3}9
In general, remember that log_{a}b = c ⇔ b = a^{c}
Logarithm Laws
You need to know that
Here are some examples:
You may be asked to find the values of expressions without the use of tables. Here, you change the base to 10 as shown in this example:
We've changed the base from 5 to 10 and now can use a calculator to find log_{5}3.
Remember: that we change from base a to base b by using this formula:
These are equations where the variable is an index, an example is 3^{x}= 6.
The steps to the solution are:
Step 1: Take logs of both sides:
So, using the law of logarithms:
log 3^{x} = log 6 | |
x log 3 = log 6 |
Step 2: Make x the subject:
Step 3: Use a calculator to find x to 3 signifcant figures (sf).
Example:
Solve the equation 2^{2x} = 5.
Step 1: Take logs of both sides
2x log 2 = log 5
Step 2: Make x the subject
Step 3: Use a calculator to find the value of x
x = 1.16 (3sf)